On Serre duality for compact homologically smooth DG algebras

2007/02/20 by D. Shklyarov, Shklyarov, D.
Mathematics · #16D90 #18E30 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16D90 #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0702590

13 pages

arxiv created 2007/02/20 · arxiv updated 2009/12/01

Abstract

The bounded derived category of coherent sheaves on a smooth projective variety is known to be equivalent to the triangulated category of perfect modules over a DG algebra. DG algebras, arising in this way, have to satisfy some compactness and smoothness conditions. In this paper, we describe a Serre functor on the category of perfect modules over an arbitrary compact and smooth DG algebra and use it to prove the existence of a non-degenerate pairing on the Hochschild homology of the DG algebra. This pairing is an algebraic analog of a well-known pairing on the Hodge cohomology of a smooth projective variety.

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